Eck Vinzenz Gregor, Donders Wouter Paulus, Sturdy Jacob, Feinberg Jonathan, Delhaas Tammo, Hellevik Leif Rune, Huberts Wouter
Division of Biomechanics, Department of Structural Engineering, NTNU, Trondheim, Norway.
Department of Biomedical Engineering, School for Mental Health and Neuroscience, Maastricht University, Maastricht, The Netherlands.
Int J Numer Method Biomed Eng. 2016 Aug;32(8). doi: 10.1002/cnm.2755. Epub 2015 Nov 26.
As we shift from population-based medicine towards a more precise patient-specific regime guided by predictions of verified and well-established cardiovascular models, an urgent question arises: how sensitive are the model predictions to errors and uncertainties in the model inputs? To make our models suitable for clinical decision-making, precise knowledge of prediction reliability is of paramount importance. Efficient and practical methods for uncertainty quantification (UQ) and sensitivity analysis (SA) are therefore essential. In this work, we explain the concepts of global UQ and global, variance-based SA along with two often-used methods that are applicable to any model without requiring model implementation changes: Monte Carlo (MC) and polynomial chaos (PC). Furthermore, we propose a guide for UQ and SA according to a six-step procedure and demonstrate it for two clinically relevant cardiovascular models: model-based estimation of the fractional flow reserve (FFR) and model-based estimation of the total arterial compliance (CT ). Both MC and PC produce identical results and may be used interchangeably to identify most significant model inputs with respect to uncertainty in model predictions of FFR and CT . However, PC is more cost-efficient as it requires an order of magnitude fewer model evaluations than MC. Additionally, we demonstrate that targeted reduction of uncertainty in the most significant model inputs reduces the uncertainty in the model predictions efficiently. In conclusion, this article offers a practical guide to UQ and SA to help move the clinical application of mathematical models forward. Copyright © 2015 John Wiley & Sons, Ltd.
随着我们从基于人群的医学转向由经过验证且成熟的心血管模型预测所指导的更精确的个体化治疗方案，一个紧迫的问题出现了：模型预测对模型输入中的误差和不确定性有多敏感？为了使我们的模型适用于临床决策，对预测可靠性的精确了解至关重要。因此，高效且实用的不确定性量化（UQ）和敏感性分析（SA）方法必不可少。在这项工作中，我们解释了全局UQ和基于方差的全局SA的概念，以及两种适用于任何模型且无需更改模型实现的常用方法：蒙特卡罗（MC）方法和多项式混沌（PC）方法。此外，我们根据一个六步程序提出了UQ和SA的指南，并针对两个临床相关的心血管模型进行了演示：基于模型的血流储备分数（FFR）估计和基于模型的总动脉顺应性（CT）估计。MC和PC产生相同的结果，并且可以互换使用以识别在FFR和CT的模型预测不确定性方面最重要的模型输入。然而，PC更具成本效益，因为它所需的模型评估次数比MC少一个数量级。此外，我们证明了有针对性地降低最重要模型输入中的不确定性可有效降低模型预测中的不确定性。总之，本文提供了一份UQ和SA的实用指南，以帮助推动数学模型的临床应用向前发展。版权所有© 2015 John Wiley & Sons, Ltd.
